Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers

Authors:
Junlin Xiong;James Lam
Affiliations:
Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong;Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

This paper is concerned with the stabilization problem for a class of discrete-time Markovian jump linear systems with time-delays both in the system state and in the mode signal. The delay in the system state may be time-varying. The delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system. We first show that the resulting closed-loop system is a time-varying delayed Markovian jump linear system with extended state space. Then a sufficient condition is proposed for the design of a controller such that the closed-loop system is stochastically stable. Finally, numerical simulation is used to illustrate the developed theory.